Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Proton decay matrix elements on lattice Jun-Sik Yoo 1 1 Department of Physics and Astronomy Stony Brook University 2019 Lattice x Intensity Frontier Workshop, BNL, Sept. 23-25, 2019 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Introduction 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Proton Decay Process p − → Π + ℓ Baryon Number Violation Haven’t been observed. Lifetime > 10 34 years Does proton even decay? 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Experimental bound Current proton decay bound in SK, (ABE et al., 2018) 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Proton Decay Process p − → Π + ℓ Baryon Number Violation Haven’t been observed. Lifetime > 10 34 years Motivated by Baryon Asymmetry Possible explanation by GUT, SUSY-GUT 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Effective operators Four-fermion effective operators p − → Π + ℓ Hadronic states : Nonperturbative computation required. 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Effective operator 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference GUT, SUSY-GUT GUT Symmetry group to be G ⊃ SU (3) C ⊗ SU (2) L ⊗ U (1) Y ♣ Coupling unification ♣ Baryon asymmetry SUSY-GUT ♣ Superpartners to particles ♣ Better unification at higher scale 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference GUT,SUSY-GUT (a) d=4 operator (b) d=5 operator (c) d=6 operator Possible BV operators in (SUSY-)GUT 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference GUT,SUSY-GUT (d) ∼ Λ GUT (e) ∼ Λ SUSY (f) ∼ Λ EW Proton decay operator at different scales Model parameters come into Wilson coefficients (a) Y qq , Y ql , Y ud , Y ue (b) M H C (c) m ˜ l , m ˜ q , triangle loop integrals, ... 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Effective operators Figure 1: Four-fermion effective operators Effective operator : O ΓΓ ′ = ( qq ) Γ ( q ℓ ) Γ ′ , ( XY ) Γ = ( X T C P Γ Y ) C := (Charge Conjugation Matrix) ℓ |O ΓΓ ′ | p � SM = C ΓΓ ¯ � Π¯ ℓ | p � GUT ∼ C ΓΓ � Π¯ v ℓ � Π | ( qq ) Γ P Γ ′ q | p � , where C ΓΓ ′ is a wilson coefficient, Π is a meson, and p is a proton. 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Decay rate The decay rate Γ is calculated from the hadronic matrix element, � Π( p ′ ) | O ΓΓ ′ ( q ) | N ( p , s ) � � ( q 2 ) − i / q � W ΓΓ ′ W ΓΓ ′ ( q 2 ) = ¯ u N ( p , s ) (1) v ℓ P Γ ′ 0 1 m N v ℓ P Γ ′ W ΓΓ ′ ( q 2 ) u N ( p , s ) + O ( m l / m N ) ¯ = ¯ v ℓ u N ( p , s ) 0 where Π a meson, N a nucleon, and W 0 , 1 decay form factor(AOKI et al., 2000). Then the decay rate is 2 � � = ( m 2 p − m 2 Π ) 2 � � p → Π + ¯ p → Π + ¯ � C I W I � � � � Γ ℓ ℓ . (2) � � 0 32 π m 3 � � p � � I 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Matrix elements on lattice 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Hadronic states Correlation function [ 1 13] 0.750 [ 2 13] C 2 pt [ 3 13] K ( t , � p ) [ 4 13] 0.725 log (C2pt) vs. t 0.700 log(C(t)/C(t+1)) � e i � p · � x � 0 | J K ( t , � x ) J † K (0 ,� 0.675 = 0) | 0 � 0.650 � x 0.625 0.600 = asymptotic states + ... 0.575 2 4 6 8 10 12 t/a p K = [0 , 1 , 1] p min Excited states at early times Ground state at late times 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Three-point function C 3 pt ( t , t ′ ) � e i ( � p ′ · � x ′ − � x ) � 0 | J Π ( x ′ ) O ( x ) ¯ q · � = J N ( x 0 ) | 0 � (Meson)-(Decay Operator)-(Proton) � x ,� x ′ p ′ ) |O| N ( � = � Π( � p ) � Π ( t ′ − t , � × C 2 pt Tr[ PC 2 pt p ′ ) ( t , � p )] p √ Z Π � Z p 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Lattice settings Lattice paramters 24 3 × 64 × 24 32 3 × 64 × 32 lattice size lattice size gauge action Iwasaki-DSDR gauge action Iwasaki-DSDR fermion DWF fermion DWF β 1.633 β 1.75 a − 1 = 1GeV a − 1 = 1 . 37GeV lattice cutoff lattice cutoff m l a 0.00107 m l a 0.0001 m h a 0.0850 m h a 0.0450 0 . 1387 0 . 1046 m π a m π a 0.5051 0 . 3602 m K a m K a m res 0.00228 m res m π L 3.3 m π L 3.3 Deflated CG 2000+1000 Deflated CG 2000+250 AMA 32+1 AMA 32+1 N cfg 102 N cfg 20(and counting) 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Kinematic Choice Energy-momentum conservation & q 2 ∼ 0 3.0 3.0 2.5 2.5 2.0 2.0 p min 1.5 p min 1.5 |p| |p| 1.0 1.0 012 002 0.5 0.5 111 001 011 011 0.0 001 0.0 111 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 q 2 a 2 q 2 a 2 π K 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Matrix elements decay form factor < K 0 |( us ) L u L | p > 0.075 0 ( p → K 0 e + ) at t sep = 8 W LL 0.070 p p = [0 , 0 , 0] p min , 0.065 W 0 a 2 0.060 p K = [0 , 1 , 1] p min 0.055 2 = 2.355 0.050 p = [0, 1, 1] 0.045 plateau fit t=3–5 0 1 2 3 4 5 6 t / a AMA 32+1, 102 configs 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Matrix elements Decay matrix elements w/ different src-sink separation { 8,9,10 } 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Matrix elements Decay matrix elements w/ different src-sink separation { 8,9,10 } 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Comparison with earlier work Bare value, but multiplicative renormalization only − → ratio can be compared with renormalized values � � W ΓΓ ′ ( Channel ) � � W norm 0 = (3) � � 0 W ΓΓ ′ ( � K + | ( ds ) Γ u Γ ′ | p � ) � � 0 � � 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Comparison with earlier work This Study + |(ud) L d R |p Aoki:2017 + |(ud) L d L |p K + |(ds) L u R |p K + |(ds) L u L |p K + |(ud) L s R |p K + |(ud) L s L |p K + |(us) L d R |p K + |(us) L d L |p K 0 |(us) L u R |p K 0 |(us) L u L |p 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Comparison with earlier study, (AOKI et al., 2017) 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
Introduction Effective operator Matrix elements on lattice Future projects Conclusion Reference Comparison with earlier work + |(ud) L d R |p + |(ud) L d L |p K + |(ds) L u R |p K + |(ds) L u L |p K + |(ud) L s R |p K + |(ud) L s L |p K + |(us) L d R |p K + |(us) L d L |p K 0 |(us) L u R |p This Study K 0 |(us) L u L |p Aoki:2017 0.0 0.5 1.0 1.5 2.0 Comparison with earlier study, (AOKI et al., 2017) 2019 Lattice x Intensity Frontier Workshop, JS Yoo Proton Decay / 41
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